MCMC variance estimators.

Author: Hai-Dang Dau

Various estimators of the asymptotic variance of a MCMC kernel, based on M chains of length P:

  • initial sequence estimator of Geyer

  • Tukey-Hanning

This may be used to estimate the (asymptotic) variance of estimates generated by waste-free SMC.


MCMC_Tukey_Hanning(X[, method, bias, ...])

MCMC Variance estimator using spectral variance method with Tukey_Hanning window.

MCMC_init_seq(X[, method, bias])

initial sequence estimator, see Practical MCMC (Geyer 1992) Let c_0, c_1, .

MCMC_variance(X, method)

param X:

a (P, M) numpy array which contains M MCMC chains of lengths P


MCMC_variance_weighted(X, W, method)

Like MCMC_variance, but each column of X has a weight W that sums to 1.

autocovariance(X, order[, mu, bias])

autocovariance_fft_multiple(X[, mu, bias])

param X:

numpy array of shape (P,M), which corresponds typically to M MCMC runs of length P each.

autocovariance_fft_single(x[, mu, bias])

param x:

numpy array of shape (n,)



AutoCovarianceCalculator(X[, method, bias])

An artificial device to efficiently calculate the autocovariances based on (possibly) multiple runs of an MCMC method.